A research drone monitors the rate of data transmission, D(t)D(t)D(t), in gigabits per hour, from a remote sensor over a 4-hour period. The transmission rate is modelled by the function
D(t)=1.25t0.5t2+4,0≤t≤4 D(t) = \frac{1.25^t}{\sqrt{0.5t^2 + 4}}, \quad 0 \le t \le 4 D(t)=0.5t2+41.25t,0≤t≤4Complete the table below, giving the values of D(t)D(t)D(t) to 3 decimal places.
| ttt | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| D(t)D(t)D(t) | 0.500 | 0.638 | 0.705 |
Use the trapezium rule, with all the values of D(t)D(t)D(t) from the completed table, to find an approximate value for the total data transmitted,
∫041.25t0.5t2+4 dt \int_{0}^{4} \frac{1.25^t}{\sqrt{0.5t^2 + 4}} \, dt ∫040.5t2+41.25tdtPractise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
